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Simple Linear Regression:

The estimated intercept is -44850 and the estimated slope is 280.76 for predicting house prices from square feet.To make predictions for inputs in square meters, what slope must you use?

Observations:

  1. Since the inputs can be converted into square meters i thought the slope would be the same.

  2. In case we change the input( since 1 square foot = .092903 square meter) I multiplied the slope with that number. Both doesnt seem to work out.

Can anyone suggest me where am I going wrong? Thanks in advance.

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1 Answer 1

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To start off, why would you expect the slope to stay the same if you adjust the scale of your independent variable (price per square feet)? If you divide your x variable by 10, your beta estimate will be multiplied by 10 to compensate for the change and still predict the same y value.

Why is this? Your beta estimate is found by $\beta = \frac{Y - \alpha}{x}$. If $\alpha$ and $y$ stay the same and you make $x$ ten time smaller, $\beta$ would be ten times larger.

Your beta estimate for predicting house prices is 280.76 per square feet. 1 square foot = .092903 square meter so we multiply 280.76 * 1 / (.092903) = 3022.077 per square meter. Intuitively this make sense, we know square meter is a bigger unit of area than square foot, thus we would expect the beta estimate to be higher.

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